{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "MultiVariateGradientDescent.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyNZpY4rsbOw2WfmvZskgV9e",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Divyanshu-ISM/Oil-and-Gas-data-analysis/blob/master/MultiVariateGradientDescent.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H2P1KrXwViAi",
        "colab_type": "text"
      },
      "source": [
        "#Gradient Descent to find the minima of a multivariable function z = f(x,y)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i5kxwj7UQudN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from mpl_toolkits.mplot3d import axes3d"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xoaT5Vm4RFAh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = np.arange(-100,101)\n",
        "y = np.arange(-100,101)\n",
        "z = x**2 + y**2"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "53wgUzHvRSXP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 375
        },
        "outputId": "289ca126-e21a-4c66-ff15-8220339f5f50"
      },
      "source": [
        "plt.figure(figsize=(8,6))\n",
        "ax1 = plt.subplot(111, projection='3d') \n",
        "ax1.plot(x,y,z)\n",
        "plt.xlabel('X values')\n",
        "plt.ylabel('Y values')"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 0, 'Y values')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f5uAz_a3RUN2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "alpha = 0.1\n",
        "\n",
        "x_r = 50\n",
        "y_r = 50\n",
        "\n",
        "z_r = [0,5000]\n",
        "\n",
        "#delz_delx = 2x\n",
        "#delz_dely = 2y\n",
        "\n",
        "while abs(z_r[-1] - z_r[-2]) >= 0.000000000001:\n",
        "  x_r = x_r - alpha*2*x_r\n",
        "  y_r = y_r - alpha*2*y_r\n",
        "  zr = x_r**2 + y_r**2\n",
        "  z_r.append(zr)\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xKmSupCCUNr0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "outputId": "129dbd05-30e4-4046-d0b2-05609ee5ca1e"
      },
      "source": [
        "print(f'1. The value of x that gives a minima is: {x_r}')\n",
        "print(f'2. The value of y that gives a minima is: {y_r}')\n",
        "print(f'3. The minimum value of of the function is: {z_r[-1]}')"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1. The value of x that gives a minima is: 8.834235323891926e-07\n",
            "2. The value of y that gives a minima is: 8.834235323891926e-07\n",
            "3. The minimum value of of the function is: 1.5608742751579976e-12\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "715pPpRyUPWJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Observe how close these values are to the real solutions. \n",
        "#Real solutions- 1. x_r = 0 , 2. y_r = 0, 3. z_min = 0 (Very close convergence)"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hVn8FWJiURIO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#End. "
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GQXRGetJUT16",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aYLbJB2gUqFh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}